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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationSat, 12 Dec 2009 07:22:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/12/t1260627957ofk5dbg318wzlts.htm/, Retrieved Mon, 29 Apr 2024 15:31:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66984, Retrieved Mon, 29 Apr 2024 15:31:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Backward Selection] [arima] [2009-12-12 14:22:51] [99bf2a1e962091d45abf4c2600a412f9] [Current]
-   P     [ARIMA Backward Selection] [Paper. Arima Back...] [2009-12-12 17:29:30] [d31db4f83c6a129f6d3e47077769e868]
- RM        [ARIMA Forecasting] [Paper. Arima Fore...] [2009-12-12 17:36:09] [d31db4f83c6a129f6d3e47077769e868]
-   P     [ARIMA Backward Selection] [Paper. Arima Back...] [2009-12-16 12:53:00] [d31db4f83c6a129f6d3e47077769e868]
- RMP     [ARIMA Forecasting] [Paper. Arima Fore...] [2009-12-16 12:59:16] [d31db4f83c6a129f6d3e47077769e868]
- RMP     [ARIMA Forecasting] [Paper. ARIMA Fore...] [2009-12-19 10:48:28] [d31db4f83c6a129f6d3e47077769e868]
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Dataseries X:
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66984&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66984&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationsar1sma1
Estimates ( 1 )0.58-0.9991
(p-val)(0.0116 )(0.007 )
Estimates ( 2 )0-0.137
(p-val)(NA )(0.6134 )
Estimates ( 3 )00
(p-val)(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & sar1 & sma1 \tabularnewline
Estimates ( 1 ) & 0.58 & -0.9991 \tabularnewline
(p-val) & (0.0116 ) & (0.007 ) \tabularnewline
Estimates ( 2 ) & 0 & -0.137 \tabularnewline
(p-val) & (NA ) & (0.6134 ) \tabularnewline
Estimates ( 3 ) & 0 & 0 \tabularnewline
(p-val) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66984&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]sar1[/C][C]sma1[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.58[/C][C]-0.9991[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0116 )[/C][C](0.007 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0[/C][C]-0.137[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.6134 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66984&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

ARIMA Parameter Estimation and Backward Selection
Iterationsar1sma1
Estimates ( 1 )0.58-0.9991
(p-val)(0.0116 )(0.007 )
Estimates ( 2 )0-0.137
(p-val)(NA )(0.6134 )
Estimates ( 3 )00
(p-val)(NA )(NA )







Estimated ARIMA Residuals
Value
-1948.65131451159
-9000.05391925435
-2479.06466562855
-14689.058235096
439.503552324479
445.371092546245
847.53558729414
-1833.49085404175
-5273.42652260205
5680.14962692571
4174.14750795916
-1392.90900261803
-5036.0147746226
-3128.24171269391
-5576.57551701459
-18166.9386409161
-5109.45237520539
-10142.7851804319
7148.81859299241
-8633.40823965558
-7622.56402425674
610.990560512562
-12882.1195409981
-12729.8896077938
9389.72222031972
2558.43018902943
-17804.9194661308
15215.1242260076
3959.00460184102
11490.4258089627
341.369625687741
1178.24025595344
1197.72339130860
3458.69298313588
-7769.79378945309
18854.9748999895
-4614.615928168
-3667.44157697201
4849.35506002396
4900.78848141619
13458.4652319889
11437.4268559328
9463.77416882255
13938.4425950781
18787.1118946825
3065.91275786329
6883.37607338714
6977.5236745886
-1075.29838745136

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-1948.65131451159 \tabularnewline
-9000.05391925435 \tabularnewline
-2479.06466562855 \tabularnewline
-14689.058235096 \tabularnewline
439.503552324479 \tabularnewline
445.371092546245 \tabularnewline
847.53558729414 \tabularnewline
-1833.49085404175 \tabularnewline
-5273.42652260205 \tabularnewline
5680.14962692571 \tabularnewline
4174.14750795916 \tabularnewline
-1392.90900261803 \tabularnewline
-5036.0147746226 \tabularnewline
-3128.24171269391 \tabularnewline
-5576.57551701459 \tabularnewline
-18166.9386409161 \tabularnewline
-5109.45237520539 \tabularnewline
-10142.7851804319 \tabularnewline
7148.81859299241 \tabularnewline
-8633.40823965558 \tabularnewline
-7622.56402425674 \tabularnewline
610.990560512562 \tabularnewline
-12882.1195409981 \tabularnewline
-12729.8896077938 \tabularnewline
9389.72222031972 \tabularnewline
2558.43018902943 \tabularnewline
-17804.9194661308 \tabularnewline
15215.1242260076 \tabularnewline
3959.00460184102 \tabularnewline
11490.4258089627 \tabularnewline
341.369625687741 \tabularnewline
1178.24025595344 \tabularnewline
1197.72339130860 \tabularnewline
3458.69298313588 \tabularnewline
-7769.79378945309 \tabularnewline
18854.9748999895 \tabularnewline
-4614.615928168 \tabularnewline
-3667.44157697201 \tabularnewline
4849.35506002396 \tabularnewline
4900.78848141619 \tabularnewline
13458.4652319889 \tabularnewline
11437.4268559328 \tabularnewline
9463.77416882255 \tabularnewline
13938.4425950781 \tabularnewline
18787.1118946825 \tabularnewline
3065.91275786329 \tabularnewline
6883.37607338714 \tabularnewline
6977.5236745886 \tabularnewline
-1075.29838745136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66984&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-1948.65131451159[/C][/ROW]
[ROW][C]-9000.05391925435[/C][/ROW]
[ROW][C]-2479.06466562855[/C][/ROW]
[ROW][C]-14689.058235096[/C][/ROW]
[ROW][C]439.503552324479[/C][/ROW]
[ROW][C]445.371092546245[/C][/ROW]
[ROW][C]847.53558729414[/C][/ROW]
[ROW][C]-1833.49085404175[/C][/ROW]
[ROW][C]-5273.42652260205[/C][/ROW]
[ROW][C]5680.14962692571[/C][/ROW]
[ROW][C]4174.14750795916[/C][/ROW]
[ROW][C]-1392.90900261803[/C][/ROW]
[ROW][C]-5036.0147746226[/C][/ROW]
[ROW][C]-3128.24171269391[/C][/ROW]
[ROW][C]-5576.57551701459[/C][/ROW]
[ROW][C]-18166.9386409161[/C][/ROW]
[ROW][C]-5109.45237520539[/C][/ROW]
[ROW][C]-10142.7851804319[/C][/ROW]
[ROW][C]7148.81859299241[/C][/ROW]
[ROW][C]-8633.40823965558[/C][/ROW]
[ROW][C]-7622.56402425674[/C][/ROW]
[ROW][C]610.990560512562[/C][/ROW]
[ROW][C]-12882.1195409981[/C][/ROW]
[ROW][C]-12729.8896077938[/C][/ROW]
[ROW][C]9389.72222031972[/C][/ROW]
[ROW][C]2558.43018902943[/C][/ROW]
[ROW][C]-17804.9194661308[/C][/ROW]
[ROW][C]15215.1242260076[/C][/ROW]
[ROW][C]3959.00460184102[/C][/ROW]
[ROW][C]11490.4258089627[/C][/ROW]
[ROW][C]341.369625687741[/C][/ROW]
[ROW][C]1178.24025595344[/C][/ROW]
[ROW][C]1197.72339130860[/C][/ROW]
[ROW][C]3458.69298313588[/C][/ROW]
[ROW][C]-7769.79378945309[/C][/ROW]
[ROW][C]18854.9748999895[/C][/ROW]
[ROW][C]-4614.615928168[/C][/ROW]
[ROW][C]-3667.44157697201[/C][/ROW]
[ROW][C]4849.35506002396[/C][/ROW]
[ROW][C]4900.78848141619[/C][/ROW]
[ROW][C]13458.4652319889[/C][/ROW]
[ROW][C]11437.4268559328[/C][/ROW]
[ROW][C]9463.77416882255[/C][/ROW]
[ROW][C]13938.4425950781[/C][/ROW]
[ROW][C]18787.1118946825[/C][/ROW]
[ROW][C]3065.91275786329[/C][/ROW]
[ROW][C]6883.37607338714[/C][/ROW]
[ROW][C]6977.5236745886[/C][/ROW]
[ROW][C]-1075.29838745136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66984&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated ARIMA Residuals
Value
-1948.65131451159
-9000.05391925435
-2479.06466562855
-14689.058235096
439.503552324479
445.371092546245
847.53558729414
-1833.49085404175
-5273.42652260205
5680.14962692571
4174.14750795916
-1392.90900261803
-5036.0147746226
-3128.24171269391
-5576.57551701459
-18166.9386409161
-5109.45237520539
-10142.7851804319
7148.81859299241
-8633.40823965558
-7622.56402425674
610.990560512562
-12882.1195409981
-12729.8896077938
9389.72222031972
2558.43018902943
-17804.9194661308
15215.1242260076
3959.00460184102
11490.4258089627
341.369625687741
1178.24025595344
1197.72339130860
3458.69298313588
-7769.79378945309
18854.9748999895
-4614.615928168
-3667.44157697201
4849.35506002396
4900.78848141619
13458.4652319889
11437.4268559328
9463.77416882255
13938.4425950781
18787.1118946825
3065.91275786329
6883.37607338714
6977.5236745886
-1075.29838745136



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 1 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 1 ;
R code (references can be found in the software module):
library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval <- arimaSelect.out[[2]][1:k,]
aic <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01) symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1) & (pval[j,i]>=.05)) symb = 'red'
else symb = 'black'
polygon(c(i+.5 ,i+.2 ,i+.5 ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix) {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i ,1+2*i ,1+2*i-.5 ,1+2*i),
c(.4 ,.7 , .4 , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated ARIMA Residuals', 1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Value', 1,TRUE)
a<-table.row.end(a)
for (i in (par4*par5+par3):length(resid)) {
a<-table.row.start(a)
a<-table.element(a,resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')